Is it enough? WSCoL is too limited for some interes1ng quality dimensions and cannot predicate on sequences of interac1ons
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- Annis Gilbert
- 5 years ago
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1 I t enouh? WSCoL too lmted for ome nteren qualty dmenon and cannot predcate on equence of nteracon Th lmt affect alo propoonal loc n eneral Addn me to propoonal loc the repone to the need of decrbn propere that lat over the ytem evoluon and order event
2 What Temporal Loc? Formalm to decrbe relaonhp amon the tate a ytem can aume durn t evoluon Tme not alway added explctly Temporal operator (toether wth the clacal connecve) decrbe an order amon event If A hold then eventually B wll hold A hold unl Alway B hold Clacal loc (wth dfferent me tructure) CTL (Computaonal Tree Loc) LTL (Lnear Temporal Loc) TL (etrc Temporal Loc)
3 CTL n a nuthell () CTL a branchn loc It evaluated on a tree tructure Very nformally: whle a ytem evolve t can evolve n many dfferent way and we could be ntereted n the extence of a behavor or n the lobal afacon The evoluon of a ytem can be een a a tree of evoluon " " "w" w" " " w" " w" " ". ""." " " " "
4 CTL n a nuthell () Temporal operator are compoed by two part Path quanfe A for All path E there Ext a path Temporal component X next tate (the next tep n the evoluon) G Globally (alway) F Eventually U Unl Not all the temporal operator are needed Some can be derved
5 CTL n a nuthell (3) " EX " EG w" " w" " " w" " w" " w" " w" " ". ""." " " " " " ". ""." " " " " Some equvalence AX A AG A EG A not EX not A not EF not A not AF not A EF A E(true U A)
6 LTL n a nuthell () It evaluated on a lnear tructure Very nformally: whle a ytem evolve t can evolve n many dfferent way but at the end t wll execute n only a poble way and we could be ntereted n tan propere that have to hold on the actual behavor (whatever ) Each LTL formula mplctly externally quanfed by unveral path quanfer Temporal operator defne a orn amon event (over the me) X next tate (the next tep n the evoluon) G Globally (alway) F Eventually U Unl
7 f ^ f ^ f ff ff f ff ^ f f f f f^ff ^ f f f E ff^ ^ fe fff fe f ff f ^f E E A E E E A = f A f ^ f f f A A defined over Krpe tructure ^ Xf F fsemanc Gf f U formally A ytem A a E A Krpe tructure w here A tranon =(SRL) ^f f f S et f the finte of tate _ A R the tranon _ E relaon _ abeln _ (that funcon label f L t he l the tate) _ ^ ^ ^ tree we _e n of a K A u The C TL t he u nfoldn rpe tructure ^ ^ _ X ^ ^ over the path π X f m ean t hat t he f ormula f h old X ^ ^ X X of t he tructure _ F X X X F F X F F ^ F F F G t here ext uch t hat G G F X G G G for a ll G G j < U U j U F t here e xt uch t hat G U U j j < j j<< j U j j < and U ju j <j < G j j j U j j< j j j < R < R j j R j < j U j < R j < j j < j jr j <j j j j j < R j LTL n a nuthell ()
8 LTL n a nuthell (3) a b Fb (not b)u(not a) X(a b) Gb Some equvalence Fa trueua Ga not F not a
9 etrc over tme We may be ntereted n tan dtance over me and not only orn amon event Whch temporal doman needed? Dcrete Dene Real How can we tate metrc propere? etrc over me allow the dener to tate repone me propere
10 An example: tmed- WSCoL We can ue t to predcate on equence of nteracon WSCoL + 4 temporal operator + temporal funcon Become(A) Unl(A B) Between(ABK) Wthn(AK) Count(A K) Semanc explaned by referrn to med word Sequence of me- tamped event that chane over me (trctly monotonc)
11 Become and Untl Become(A) Unl(AB)
12 Between and Wthn Between(AB6) Wthn(A6)
13 Count Count(B36) In 5: Count(Become(B) 36) = Become(Count(B 36) = 3) fale
14 Dynamo
15 Aynchronou ontorn Two nd of ubcrpon to the AcvePool Data- chane Data- value Bounded temporal predcate and funcon ue data- value ubcrpon Unl(AB) Chec B at preent me and f t not vald t chec A. If A not vald the formula fale. If A vald t chec f B become true before A chane. Between(ABK) Save the me tamp of the frt valdty of A or B. Stop accepn value a oon a t receve a value me- tamped beyond K. Chec f the formula hold n the penulmate value receved.
16 Aynchronou ontorn Wthn(AK) Chec the value of A. Wat for a chane n A contantly checn the me tamp. Stop when t receve a value that me- tamped beyond K. Count(A K) Increment a local counn varable each me t receve a value n whch A true. Stop when t receve a value that me- tamped beyond K.
17 An operatonal formalm Büch Alternatn Automata (BAA) are Büch Automata wth both unveral and extental modalte ASA are BAA enrched wth a et of bounded tme counter ASA accept tme-tamped nfnte word: A letter nclude Tme-tamp The current value of all the nternal and external varable and event A fnte number of pat value of the varable The evaluaton of ALBERT functon Letter are collected when a value chane
18 Example Alw(A Between(BCK))
19 A Krt lmtaton
20 Lmted ASA (td mode) Equvalent to ASA Duplcate are avoded f not needed
21 Crtcal mode Crtcal mode = the dcovery of a volaton caue a complete halt of the ytem and thu of the verfcaton actvte Wthn(AK): If A occur n () t atfe both the ntance of Wthn(AK)
22 An example
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